Problem: Reduce to lowest terms: $ \dfrac{9}{2} \div - \dfrac{2}{5} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{2}{5}$ is $- \dfrac{5}{2}$ Therefore: $ \dfrac{9}{2} \div - \dfrac{2}{5} = \dfrac{9}{2} \times - \dfrac{5}{2} $ $ \phantom{ \dfrac{9}{2} \times - \dfrac{5}{2}} = \dfrac{9 \times -5}{2 \times 2} $ $ \phantom{ \dfrac{9}{2} \times - \dfrac{5}{2}} = \dfrac{-45}{4} $